Is there a rigorous proof that AGI is possible, at least, in theory?
A strong reason why people think the mind can be implemented on a Turing Machine stems from the Computational Theory of Mind (CTOM), which is the leading theory of mind for now.
There are lots of reasons for supporting the CTOM, one of which being that the language of belief/desire psychology (propositional attitudes over mental representations) seems to fit nicely to a computational framework.
But most simply is that the computation analogy is very helpful in fields such as psychology and neuroscience. When we know of an input/output pair, but don't know how it is implemented, we could say &quot;its performing the relevant computation&quot;.
And since Turing showed that any computation can be performed on an appropriate Turing Machine, the natural extension is that the mind can be implemented on a computer.
However, the CTOM is more of a useful idea than a complete theory. We still don't know how to analyze thought in a logical syntax, which can be implemented in a computer. And we also don't know how/why &quot;computation&quot; (whatever that means in this sentence) is performed in the brain.